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Journal of Geometry

, 110:19 | Cite as

A characterization of the set of internal points of a conic in PG(2,q), q odd

  • Stefano Innamorati
  • Fulvio ZuanniEmail author
Article
  • 25 Downloads

Abstract

A point P not on a non-degenerate conic C in PG(2, q), q odd, is called internal to C if no tangent line to C contains P, external otherwise. The set of internal points of C is a \(\frac{q(q-1)}{2}\)-set of type \((0,\frac{q-1}{2},\frac{q+1}{2})\). In this paper, we classify all \(\frac{q(q-1)}{2}\)-sets of class [0, mn] having exactly two kinds of outer points.

Keywords

Sets of class \([0, m, n]\) three character sets conics 

Mathematics Subject Classification

51E20 51E21 

Notes

Acknowledgements

We are grateful to the anonymous referee for useful suggestions which noticeably improved the presentation of the paper.

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Industrial and Information Engineering and EconomicsUniversity of L’AquilaL’AquilaItaly

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